MATERIAL RESPONSE AT MICRO-, MULTI-, AND MACROSCALES

作者：Grigoriu M^*

来源：International Journal for Multiscale Computational Engineering, 2016, 14(3): 237-254.

DOI：10.1615/InGMultCompEng.2016015857

• continuum mechanics
• micromechanics
• model calibration
• multiscale models
• random field microscale models
• stochastic equations

Three examples are used to illustrate relationships between material responses at different scales, practical use of these relationships, and differences between microscale and multiscale solutions. In the first example, force-displacement constitutive laws are developed for rods with random, linear/nonlinear, small-scale stress-strain relationships. It is shown that the continuum mechanics constitutive law may or may not match, on average, the corresponding microscale-based law depending on material properties at small scale. In the second example, it is assumed that a spatial correlation parameter of the microscale conductivity field is unknown. Because this parameter cannot be measured directly, measurements of the apparent conductivity on laboratory-scale specimens are used to identify this microscale model parameter. In the third example, one-dimensional conductivity problems are used to quantify differences between microscale and multiscale solutions that relate solely to approximate representations of the random field describing the microstructure conductivity.

• 出版日期2016